Problem: Factor completely. $x^3-8x^2-2x+16=$
Explanation: Notice the expression has four terms. In cases like this, we will try to factor the expression by grouping. Finding common factors Before we factor, we need to find the common factors for the two pairs of terms. The first pair is $x^3$ and $-8x^2$. Their greatest common factor is ${x^2}$. The second pair is $-2x$ and $16$. Their greatest common factor is $2$. Since the first term is negative, let's factor out ${-2}$. Factoring by grouping Let's factor these common factors out: $\begin{aligned} &\phantom{=}x^3-8x^2-2x+16 \\\\ &={x^2}(x)+{x^2}(-8){-2}(x){-2}(-8) \\\\ &={x^2}(x-8){-2}(x-8) \end{aligned}$ Now we are left with a common factor of $(x-8)$, so we can factor it out: $\begin{aligned} &\phantom{=}x^2C{(x-8)}-2C{(x-8)} \\\\ &=C{(x-8)}(x^2-2) \end{aligned}$ In conclusion, this is the completely factored expression: $(x-8)(x^2-2)$